PRP Records

Probable Primes Top 10000

(172213 PRPs in the top)


What is a PRP ?

A PRP is a probable prime number, a number that nobody knows how to prove or disprove its primality.
Here are some criterions that can be used to recognize these numbers :

- N does not have any prime factor up to 2^32.
- N cannot be trivially written into a product.
- Take 3 square-free consecutive bases such that (b1/N)=(b2/N)=(b3/N)= -1. N should be such that b1^((N-1)/2)=b2^((N-1)/2)=b3^((N-1)/2)= -1 (mod N).
- Take a prime base such that (b/N)= -1 and b<>b1<>b2<>b3. N should pass the strong test in base b.
- or more (if someone has got an idea) !!!


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1-250   251-500   501-750   751-1000   1001-1250   1251-1500   1501-1750   1751-2000   
2001-2250   2251-2500   2501-2750   2751-3000   3001-3250   3251-3500   3501-3750   3751-4000   
4001-4250   4251-4500   4501-4750   4751-5000   5001-5250   5251-5500   5501-5750   5751-6000   
6001-6250   6251-6500   6501-6750   6751-7000   7001-7250   7251-7500   7501-7750   7751-8000   
8001-8250   8251-8500   8501-8750   8751-9000   9001-9250   9251-9500   9501-9750   9751-10000   


Rank Probable prime Digits (> 30000) Who ? When ?
9001(598*10^49999-31)/950001Robert Price02/2017
900210^49999+9170150000Patrick De Geest03/2005
900310^50000-19430350000Patrick De Geest02/2009
9004(2^74207281/10^948782)%10^5000050000Michael Vang04/2016
9005(2^57885161/10^11608093)%10^5000050000Michael Vang05/2016
9006(2^43112609/10^788658)%10^5000050000Michael Vang05/2016
9007(2^42643801/10^3670320)%10^5000050000Michael Vang05/2016
9008(2^37156667/10^412682)%10^5000050000Michael Vang05/2016
9009(2^32582657/10^7836670)%10^5000050000Michael Vang05/2016
9010(2^24036583/10^3069021)%10^5000050000Michael Vang05/2016
9011(2^25964951/10^5214128)%10^5000050000Michael Vang05/2016
9012(2^13466917/10^157937)%10^5000050000Michael Vang05/2016
9013(2^20996011/10^6193479)%10^5000050000Michael Vang05/2016
9014(2^6972593/10^381525)%10^5000050000Michael Vang05/2016
9015(2^30402457/10^1629036)%10^5000050000Michael Vang05/2016
9016(2^3021377/10^702316)%10^5000050000Michael Vang05/2016
9017(2^1398269/10^37827)%10^5000050000Michael Vang05/2016
9018(2^2976221/10^767789)%10^5000050000Michael Vang05/2016
9019(2^859433/10^42285)%10^5000050000Michael Vang06/2016
9020(2^1257787/10^119173)%10^5000050000Michael Vang06/2016
9021(2^756839/10^136257)%10^5000050000Michael Vang06/2016
90222*10^49999+36350000Makoto Morimoto09/2016
902310^49999-414949999Patrick De Geest02/2009
902410484^12433-12433^1048449988Norbert Schneider07/2013
90252^166052+14549987Lelio R Paula01/2011
9026(10^50001+10936)/(2^3*19*241*5872003*15974507)49983Makoto Morimoto09/2016
90271111*2^166022-55549981Henri Lifchitz02/2005
902811^47993+3049980Lelio R Paula10/2012
90292^166000-7879549971Lelio R Paula07/2011
903013517!-13517#+14997003/2005
90322^165995-11322749970Enzo Doria07/2014
9031(12227^12227+1092)/5/11/17/37^249970Makoto Morimoto07/2016
903317^40609+1449968Lelio R Paula11/2012
9034(1257656^8192+1)/6553749963Syoichiro Yamada06/2008
9035(3^104735-8)/149319993149963Lelio R Paula03/2012
90362^165969-11271149962Enzo Doria06/2014
90372^165910-760549944Lelio R Paula04/2009
903836313!3-5904949942Robert Price12/2015
90392^165884-4549937Lelio R Paula08/2010
9040(1246892^8192+1)/6553749933Syoichiro Yamada06/2008
90413^104654+10449933Lelio R Paula07/2012
90429035^12622+12622^903549932Norbert Schneider01/2016
9043(22699*2^165838+1)/328749924Lelio R Paula05/2014
90446^64149-8549918Lelio R Paula06/2012
9045(7*10^49913+71)/349914Robert Price03/2016
90462^165799-11481749911Enzo Doria05/2015
90472^165789+3549908Lelio R Paula08/2010
90482^165783-12149906Lelio R Paula01/2011
90492^165760-11264949899Enzo Doria06/2014
9050(11*2^165758+1)/13549898Lelio R Paula01/2012
90512^165747+6349895Lelio R Paula04/2009
9052(7*10^49893-13)/349894Robert Price06/2016
9053298^20163-20163^29849888Norbert Schneider08/2015
9054(49885^49885)/(10^184474)49885James G. Merickel08/2015
905517^40540+3649883Lelio R Paula11/2012
9056(12211^12211+4312)/13/17/31/1297/1483/1627/9923/3643349882Makoto Morimoto07/2016
90572^165676-11294949874Enzo Doria06/2014
9058(12203^12203+992)/1149867Makoto Morimoto07/2016
90592^165581-74549845Yves Minet01/2012
90602^165576+7482149844Enzo Doria04/2016
906113318^5527+5527^1331849843Hans Havermann04/2016
90632^165561-215549839Yves Minet08/2013
9062(12197^12197+1755)/2^449839Makoto Morimoto07/2016
90647406^12879+12879^740649837Norbert Schneider03/2016
90658530^12677+12677^853049833Norbert Schneider01/2016
9066(3^52222-69)^2-7149833Jorge Menendez02/2017
906712^46175+2949832Lelio R Paula10/2012
90682^165488-1296949817Enzo Doria10/2012
90692^165473+5890549813Lelio R Paula04/2009
907020^38284+4949809Lelio R Paula11/2012
90723^104388-2049806Lelio R Paula07/2012
9071(10^49806+119)/349806Serge Batalov12/2014
9073(1202206^8192+1)/6553749803Syoichiro Yamada06/2008
9074(4*10^49801+11)/349802Erik Branger05/2013
90755^71240-1547649795Enzo Doria02/2013
90767*3^104334-449781Lelio R Paula03/2014
9077(136*10^49774-1)/949776Serge Batalov12/2014
90783^104297+868049763Lelio R Paula07/2012
9079(F(10)^28579-F(9)^28579)/F(8)49737Wayne Halsdorf03/2010
9080(3^104243+1)/449736Kamil Duszenko05/2004
9081(10223*2^165183+1)/5549728Lelio R Paula05/2014
90826^63895+10149720Lelio R Paula06/2012
90833^104194+10049714Lelio R Paula07/2012
9084U(356793)49710Serge Batalov03/2015
908513321^5388+5388^1332149707Hans Havermann04/2016
908612166^12166+56549700Henri Lifchitz11/2004
9087(89*10^49689-53)/949690Erik Branger05/2013
9088(1163126^8192+1)/6553749685Syoichiro Yamada06/2008
908911^47709+4249684Lelio R Paula10/2012
9090(35*10^49682+1)/949683Serge Batalov05/2010
9091(12163^12163+1194)/37/19349683Makoto Morimoto07/2016
90923^104124+9249680Lelio R Paula07/2012
90942^165025+16502949678Henri Lifchitz04/2005
909314063^3408+3408^1406349678Hans Havermann04/2016
9095(2^165031+3)/4843949675Lelio R Paula01/2012
9096(7*2^165020-1)/26149675Lelio R Paula01/2014
90982^165000+522749670Lelio R Paula05/2011
9097(12161^12161+765)/2/13/29/277/31149670Makoto Morimoto07/2016
9099(110051^9851+1)/11005249660Faysal YAtim09/2007
91002^164962-63979149659Paul Bourdelais11/2012
910110^49657+3149658Robert Price01/2011
910210^49657-1289949657Patrick De Geest01/2012
91032^164937-19349651Lelio R Paula01/2011
910421^37549-20^3754949649Jean-Louis Charton02/2012
91051417^15754+15754^141749647Serge Batalov05/2014
9106(12157^12157+2611)/2^5/11/13/1019/48197/31440749643Makoto Morimoto07/2016
910712^45999+2549642Lelio R Paula10/2012
9108(3^104040+7)/849639Lelio R Paula03/2012
91092^164882-101749635Lelio R Paula06/2008
9110(3^104053-8)/38183002074345549632Lelio R Paula03/2012
911111^47658-18049631Enzo Doria07/2012
91122^164859-123749628Yves Minet08/2012
911317^40331+9849626Lelio R Paula11/2012
91141638^15437+15437^163849620Serge Batalov05/2014
9115113^24160+11249603Norbert Schneider09/2013
911613^44527+1649601Lelio R Paula11/2012
911783^25844+8249597Norbert Schneider01/2013
9118(12143^12143+1306)/3/7/5949593Makoto Morimoto07/2016
9119114667#-p(114667)49591Henri Lifchitz03/2007
91202^164731-183384749589Enzo Doria05/2015
9121(625^17737+1)/62649588Richard Fischer06/2013
91222^164714+2983549584Lelio R Paula11/2011
91237*10^49580-6949581Robert Price01/2017
91247*5^70922+449574Lelio R Paula09/2014
9125(229*10^49571-1)/349573Robert Price12/2016
9126277^20295-29049571Enzo Doria06/2012
91272^164662-11288349569Enzo Doria06/2014
9128(1125424^8192+1)/6553749568Syoichiro Yamada06/2008
91296^63698-3549567Lelio R Paula06/2012
9130(2^164652-3)*6-749566Gilbert Mozzo04/2016
9131(11*10^49552+43)/949553Erik Branger05/2013
91322^164606+4349552Lelio R Paula08/2010
91332^164598-11311149549Enzo Doria07/2014
913411^47575-810049545Enzo Doria02/2013
91359420^12467-12467^942049545Norbert Schneider07/2013
91362^164581-81925349544Paul Bourdelais11/2012
91379001^12528-12528^900149540Norbert Schneider11/2016
9138(lucasV(1,2,329135)+2)/(5^2*179*10247)49533Mike Oakes02/2017
9139(4*10^49529-31)/949529Erik Branger05/2011
914013875^3712+3712^1387549529Hans Havermann03/2016
91417^58604-6249527Lelio R Paula06/2012
91422^164508+10549522Lelio R Paula04/2009
914324^35878-93749520Enzo Doria03/2013
9144(89*10^49516-17)/949517Erik Branger05/2013
91452^164478-16749513Lelio R Paula01/2011
914613^44446+3049511Lelio R Paula11/2012
91472^164466-79024149510Paul Bourdelais11/2012
9148-lucasV(-1,2,328901)49505Mike Oakes01/2017
9149(21*2^164421-1)/53349495Lelio R Paula01/2014
915035^32052-20649491Enzo Doria03/2013
91513^103726-1187849490Enzo Doria02/2013
9152(3^103726+7)/51249488Lelio R Paula03/2012
9153(12119^12119+6270)/1349487Makoto Morimoto07/2016
915410^49484+1653749485Patrick De Geest01/2016
915610^49484-10^5384-149484Serge Batalov01/2011
915510^49484-9153949484Patrick De Geest01/2016
91573*2^164365-749480Lelio R Paula02/2014
9158(7^58543-5^58543)/249475Robert Price05/2012
91598482^12591+12591^848249464Norbert Schneider11/2015
9160(29*2^164309-1)/2090749460Lelio R Paula01/2014
9161(12113^12113+3627)/2^2/5/19/1449629949451Makoto Morimoto07/2016
91625^70746-1601649450Enzo Doria02/2013
9164(2^164258+9)/1349446Lelio R Paula01/2012
91632^164255-11268749446Enzo Doria06/2014
9165(21*2^164222-1)/171749434Lelio R Paula01/2014
91662^164212+1270549433Lelio R Paula11/2011
91673*2^164205+749432Lelio R Paula02/2014
91682^164203+57729457549431Lelio R Paula02/2013
9169(12109^12109+2534)/3^2/23/24763/78102149430Makoto Morimoto07/2016
9170Pell-LucasQ(129127)/249427Eric W. Weisstein05/2006
91712^164187+769549426Lelio R Paula11/2011
91723^103585-2649423Lelio R Paula07/2012
9173(3*2^164194+1)/1425501749421Lelio R Paula07/2012
917410^49415+7683749416Patrick De Geest01/2016
917710^49415-6^49415-4^49415-149415Mike Oakes01/2010
917510^49415-3281349415Patrick De Geest01/2016
917612943^6574+6574^1294349415Hans Havermann02/2016
9178(6^63497-61)/2549409Lelio R Paula05/2014
917911376^12181+12181^1137649407Norbert Schneider12/2013
91802^164110-1749403Lelio R Paula08/2010
918112^45773+4149398Lelio R Paula10/2012
91822^164090+425749397Lelio R Paula04/2009
9183(12101^12101+1403)/2^4/193/349/160231/692768949389Makoto Morimoto07/2016
91842^164046+2549383Lelio R Paula01/2009
9185(24737*2^164045+1)/590658549381Lelio R Paula05/2014
9186(12097^12097+1922)/3/139/225340949380Makoto Morimoto07/2016
91885^70640-1829649376Enzo Doria02/2013
9187(9179*2^164010-1)/549376Lelio R Paula03/2015
9189(-lucasV(1,2,328052)+2)/10896149372Mike Oakes02/2017
91909*2^164002-749371Lelio R Paula02/2014
91915^70626-4449366Lelio R Paula06/2012
919211^47396-105049358Enzo Doria11/2012
9193(13*2^163956+1)/749356Lelio R Paula07/2012
91952^163934-13549350Lelio R Paula01/2011
91943^103431+2049350Lelio R Paula07/2012
919613^44300+2249348Lelio R Paula11/2012
9197(2^163904+3)/749340Lelio R Paula01/2012
91982^163872+1291549331Lelio R Paula11/2011
9199130^23332-12949323Norbert Schneider03/2015
92007^58357-3849318Lelio R Paula06/2012
92017760^12677-12677^776049312Norbert Schneider01/2017
920213^44265-249309Lelio R Paula11/2012
9204(19*2^163785+1)/204349303Lelio R Paula01/2012
92032^163781-174149303Yves Minet09/2012
92054*5^70529+349299Lelio R Paula09/2014
9206(2^163742-3)/13149290Lelio R Paula01/2012
92075^70514-1721649288Enzo Doria02/2013
92082^163727-174149287Yves Minet09/2012
9209Linear(0,1,1,-1,327433)49283Henri Lifchitz04/2007
92105^70498-1757649276Enzo Doria02/2013
9211(12073^12073+1070)/3/13/3106349274Makoto Morimoto07/2016
92122^163667+7211349269Enzo Doria04/2016
92135^70484-1769649267Enzo Doria02/2013
9214(12071^12071+4263)/2/101/1148949265Makoto Morimoto07/2016
92157^58293+6649264Lelio R Paula06/2012
9216(52*10^49261-1)/349263Robert Price02/2017
92172671^14376-11449262Enzo Doria06/2012
9218(15185*2^163636-1)/20949262Lelio R Paula03/2015
92192^163630+18349258Lelio R Paula01/2011
92202^163560+1549237Lelio R Paula08/2010
92213^103189+11049234Lelio R Paula07/2012
9222(41*10^49233+31)/949234Erik Branger05/2013
9223(1023052^8192+1)/6553749229Syoichiro Yamada05/2008
92242*10^49216+9349217Robert Price07/2016
92252^163453+88549205Lelio R Paula10/2011
9226(67607*2^163432+1)/349203Lelio R Paula05/2014
922715^41835-4649202Lelio R Paula11/2012
922810^49190+4550749191Patrick De Geest01/2016
923010^49190-601865949190Marisa Kirisame02/2015
922910^49190-15443149190Patrick De Geest01/2016
92312^163385+9439549184Henri Lifchitz01/2005
92322^163382-202149183Yves Minet03/2013
9234(55*10^49169-1)/949170Ray Chandler02/2012
92332^163336-1517749170Enzo Doria04/2013
92358323^12542-12542^832349169Norbert Schneider11/2016
9236(10^49165-991)/949165Serge Batalov07/2010
92377^58169-6^(58169+1)49159Robert Price06/2016
9239(F(5)^70327-F(4)^70327)/F(3)49157Wayne Halsdorf01/2010
9238(5^70327-3^70327)/249157Robert Price08/2011
92402^163283+5461549154Lelio R Paula04/2009
924118388^471+471^1838849152Anatoly F. Selevich12/2006
9242(12043^12043+799)/2/15749142Makoto Morimoto07/2016
924314^42875+6949141Lelio R Paula11/2012
9244(2^163243+9)/1749140Lelio R Paula01/2012
9245(F(770)^307-F(769)^307)/F(768)49136Wayne Halsdorf02/2010
9246(12041^12041+467)/2^2/23/4749132Makoto Morimoto07/2016
92475^70290-1944649131Enzo Doria03/2013
9248(F(760)^311-F(759)^311)/F(758)49130Wayne Halsdorf02/2010
92495^70286-2004649128Enzo Doria03/2013
925012^45519-9149124Lelio R Paula10/2012


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: March, 26 2017 17:51 (Time in France)

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